Use the IQR to determine if any of the data in the data set are outliers. {23,80,43,23,0,20,23,23,20,28} Any data value less than or greater than are outliers.

Answer 1

First put the variables in order:

0,20,20,23,23,23,23,28,43,80

There are 10 values, so the 1st quartile is the (10+1)/4 = 2.75th value, so the mean of the 2nd and 3rd values = (20 + 23)/2 = 21.5

The 3rd quartile is the (10 + 1) * 3/4 = 8.25th value, so the mean of the 8th and 9th values = (28 + 43)/2 = 35.5

The IQR = 3rd quartile - 1st quartile = 35.5 - 21.5 = 14

Values beyond Q1 - 1.5 IQR = 21.5 - 1.5 * 14 = 0.5

and Q3 + 1.5 IQR = 35.5 + 1.5 * 14 = 56.5 are considered outliers.

Thus there are two outliers: 0 and 80